The plain tuna sandwich is the tinned-tuna baseline with nothing added to soften the fact of it, and that bareness is the whole identity. Drained tinned tuna, a measured amount of mayonnaise to make it cohere, salt and pepper, soft bread, butter underneath: there is no sweetcorn, no cucumber, no onion, no salad leaf doing structural or textural work. This is the form before any of the named variations branch off it, the lunchbox default everything else is measured against. It succeeds or fails entirely on the fish and the bind, because there is nothing in the build to distract from either, and that is exactly why it is both the most common tuna sandwich in the country and the one most often made badly.
The craft is the bind and only the bind. Tinned tuna comes out of the tin compacted and a little dry, so it has to be flaked apart and then held with just enough mayonnaise to make the flakes cling without turning to a wet, sliding paste. Too little and the filling falls out of the sides in dry crumbs the moment the sandwich is cut; too much and it slumps into a slick that soaks the bread from the centre out. The fix in the plain version is not a crunchy vegetable, because there isn't one here, but precision in the ratio and seasoning that actually reaches the fish, salt and pepper worked through the mix rather than scattered on top. The bread is soft white and plain so it carries rather than competes, the butter seals the crumb against a filling that is slightly wet by design, and the mixture is spread evenly to the edges so every bite is the same rather than dry bread at one end and a damp clump at the other.
The variations are the additions that each turn the plain form into something with its own name. Sweetcorn for a pop of sweetness and texture is the lunchbox default; cucumber adds a watery crispness; red onion brings a sharp bite; a salad of leaf and tomato pushes it toward a fuller sandwich; melted cheese sealed over it under a grill changes it entirely. Each of those is a build with its own logic rather than a tweak to this one, and each deserves its own article rather than being crowded in here.